Clustering Feature

Part of a CF-Tree which is used in the BIRCH algorithm.

It is a 3D summarizing statistic about the current Clusters.

CF=(n,LS,SS)

where $n$ is the number of data points in the cluster, $LS$ is the linear sum of the points in the cluster and $SS$ is the square sum of the points in the cluster.

This statistic allows to derive some useful information about a cluster.

Centroid:

\frac{LS}{n}

Radius:

\sqrt{ \frac{nSS-2LS^2+n}{n^2} }

Diameter:

\sqrt{ \frac{2nSS-2LS^2}{n(n-1)} }

A nice way of merging two clusters is to just add the two CFs of two clusters.

Example

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